Can I paint and sculpt with the same stroke?
The short answer (unfortunately) is "no."

The slightly longer answer is that you might be able to do it with normal maps and textures, but not with a brush-like interface. Dynamic Paint is baked, not live, so you could theoretically make a brush, but you'd have to animate it rather than use it interactively.

Normal maps and displacement maps might create the effect you want, but also not really interactively.

Sculpting is the interaction you want, but there's nothing yet that lets you sculpt and paint at the same time.

Incidentally, you should check out the non-Blender tool Verve Painter by Timur Baysal. It uses a GPU fluid sim to make digital painting a bit more realistic, and a lot more awesome. And it does some impasto stuff like you're thinking of.